Interesting, because on my test run with the current balance numbers I took a game-just-created H-S-FF in there and won without losing either base, and didn't even spend the unlock points I gained during it until after the scenario.
One thing was to get to the front and save as many of the allied ships as I could with projected shadow shields and stay out there mitigating damage and putting a dent in the dysons where I could (did an all-laser loadout since dysons are Heavy). The allies reached a critical mass of ships that would just plow through the dysons. Later on the number of simultaneous dysons increased to the point that my allies' line broke and we fell back on the first starbase, but at that point we were able to hold out long enough.
I figured that if I could do it (I'm not actually that great at these things) with a brand new champion without even falling back on the larger starbase, y'all could at least win, particualrly with upgrades